Let us consider the next problem definition: a set of identical robots denoted \(R=\lbrace r_1, r_2, \ldots , r_{|R|}\rbrace \)  evolves in an known and static 2D environment. The robots are assumed omnidirectional and of negligible size, i.e., each is a fully actuated point. The environment captures several convex polygonal shapes, denoted as regions of interest (ROI) and labeled with elements from the set \(\mathcal {Y} = \lbrace y_1,y_2,\ldots , y_{|\mathcal {Y}|} \rbrace \) . These regions can be both disjointed and overlapped. Furthermore, based on these polygonal shapes, we assume that the environment is partitioned into a set of regions also called cells, for example by using a cell decomposition method [1]}, [2]}. Each cell entirely belongs to the same region(s) of interest, or it is included in the area not covered by any region of interest (free space). The advantage of this representation lies in obtaining an abstract model of the environment, e.g., Petri net model, which captures the entire space data, being invariant with respect to the number of robots.
